Activity 6

In this activity, you will learn about how production systems
work by experimenting with a program which implements a
simple production system model of meter assignment.
As with earlier activities, you are free to collaborate with other
students in the class, as long as you let us know.

To learn about the model and how to run it, see
this page from the lecture.

For each of the following periodic patterns, create the pattern
(option 0 in the program menu) and run the production system for
60 epochs (select option 1 in the program menu 3 times).

Pattern A: (1 1 0)

Pattern B: (1 1 0 0)

Pattern C: (1 1 1 1 1 0 0 0)

Pattern D: (1 1 1 0 0 1 0 0)

Pattern E: (1 0 1 0 1 1 1 0)

Pattern F: (1 1 1 0 0 1 0)

Pattern G: a pattern of your own choice with period
no greater than 8

Because there is some randomness in the way rules are selected,
you may want to run a pattern twice.
Then answer the following questions:

What sort of meter would people assign to the pattern?

That is, where would the perceived beats of different strength
underlying the pattern be?
For example, for the repeating pattern (1 1 1 0), people would
place accents on the first and third beats (the beginning
and end of a run), one stronger than the other:

2 0 1 0 2 0 1 0 ...

For the repeating pattern (1 0 1 0 1 1 1 1), people would place
accents on every other beat, accenting every fourth beat more and every
eighth beat even more, for example:

3 0 1 0 2 0 1 0 3 0 1 0 2 0 1 0 ...

Note that there is often more than one possible meter assignment
for a pattern?

How difficult for people is this pattern compared to the others?

Recall that patterns are difficult to assign meter to
when there is a conflict between
grouping and meter, that is, when the places that are accented because
of how the events are grouped are not equally spaced.
For example, the above patterns are relatively easy, but
the pattern (1 1 0 1 1 0 1 0) is difficult because the
grouping would lead one to accent things in this way:

1 0 0 1 0 0 1 0

or

0 1 0 0 1 0 1 0

But this leaves the distances between the accents unequal.

How well does the production system assign meter to
the pattern? What mistakes does it make?

To assess the performance of the production system, you will
need to look at the working memory after you run the system on
the pattern.
The last line of the "interpreted" working memory shows the
strengths for each of the 24 time steps in the sequence.
Remember that the pattern is repeated several times in the sequence.
If you can, figure out a way to combine the information from
the different repetitions of the pattern.

How well is the supposed difficulty of the pattern reflected
in the performance of the production system?
That is, does the model have more trouble with patterns which
are more difficult for people?

There are two ways in which we might expect to see greater
difficulty for the network.
First, it may take the network longer to find a suitable meter
for a pattern.
Second, it may not settle on one stable meter. Instead it may
show different beat assignments over different places within
the sequence of 24 time steps, or it may vary from one cycle
of the program to the next.
To look for evidence of both of these, you will need to
compare the performance after 20, 40, 60, and 80 cycles for the
different patterns.

Suggest two ways in which you think the model could be improved
so that it comes closer to human performance.
These could involve the rules themselves, the way in which
rules are selected on each cycle, or the way in which patterns
are represented.
Be as specific as possible, explaining why you believe these changes
would improve the performance.